I tend to procrastinate. So it wasn't until a year and
a half out of college that I began to think hard about
pursuing a career.

In
high school and college my main focus had been mathematical,
first on the math team at Grissom High School (Huntsville,
AL), then in the physics program at Princeton University.
However, I had realized near the end of college that an
academic career wasn't going to happen.

Now, after pursuing various jobs and projects, I wanted
to find something to do which was engaging, paid well, and
had at least some mathematical side to it.

What
I found was the field of arbitrage trading. Arbitrage,
pronounced "AR-bi-trazh," means executing more
than one trade such that 1) there is little or no risk,
and 2) there is some positive value.

For
example, suppose that at a farmer's market, three apples
could be swapped for two bananas, three bananas could be
swapped for two peaches, and three peaches could be swapped
for seven apples. Then I could take twenty-seven apples,
turn them into eighteen bananas, turn the bananas into twelve
peaches, and turn the peaches into twenty-eight apples.

After
all is said and done, I've earned an extra apple for my
efforts, by taking advantage of the fact that the swap rates
between the different fruits aren't exactly right---the
market has a slight anomaly. Until the farmers adjust their
swap rates, I can execute my series of trades over and over
again, netting an extra apple each time.

Of course,
in the real markets, anomalies as simple as this rarely
occur, and are quickly eradicated when they do. Intense
competition from arbitrage traders forces all securities
to stay very close to fair valuations: the market is what
economists would call efficient.

Trading
takes a lot of different forms. At first, I was standing
in a "pit" on the floor of the Chicago Board Options
Exchange, wearing a brightly colored jacket and waving my
arms to get a broker's attention. Later, I sat in front
of a bank of computer monitors, directing split-second trades
over the phone. In both cases, however, the underlying idea
was he same: to exploit the mathematical relationships between
different stocks or bonds or options or stock indexes.

That
isn't to say it's all about the math. In many trading situations,
the mathematical relationships are well-understood, and
what matters are things like speed, attention to detail,
and gamesmanship. From moment to moment, this type of trading
closer resembles a race-to-the-buzzer game show than a math
test.

Other
types of trading are more cerebral, focused on extensive
analysis to extract the relationships underlying security
prices. The pricing of options---securities which grant
the holder the right, if so desired, to buy a stock at a
specific price at a specific price---has inspired a wealth
of mathematical research. The 1997 Nobel Prize went to two
economists who pioneered a key options pricing model based
on partial differential equations. And the field has expanded
enormously since their 1973 work, with new models continuing
to proliferate in answer to ever-deeper questions. Further
afield, areas like bond analysis rest on a deep mathematical
foundation.

Traders
aren't mathematicians, however. Rather, they are skilled
users of mathematical models, often developed by quantitative
researchers at the trader's firm. However elaborate, models
always fail to capture the human side of the equation -
much as poker-playing software can calculate probabilities,
but can't infer an opponent's weak hand from her demeanor.

For
most types of trading, a solid math background at the college
level is crucial. Coursework in finance and economics is
also useful. For those more inclined to quantitative research
rather than trading, graduate study in math or science may
be required.

Trading
is in many cases a very competitive, intense enterprise.
Those who like games and don't mind stress will often excel.
However, building relationships is also a key component,
and people skills are a must.

If you're
seriously interested in trading - or finance more broadly
- talk to as many people close to the industry as you can.
Opportunities range from large investment banks (most of
which have large trading operations) to small "boutique"
operations with fewer than 100 employees. Use of headhunters
is also an important way to gain exposure to Wall Street
firms.

Contact
the editor if you
know people who would like to write about their careers.